Assessment of some iterative methods for non-symmetric linear systems arising in computational fluid dynamics

Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme.     

Weak type (1, 1) inequalities of maximal convolution operators

In this paper we study the behavior of the constants which appear in the weak type (1, 1) inequalities for maximal convolution operators by means of discrete methods. One of the first applications of these techniques will give us a very simple proof of the ergodic theorem. We also present partial results in order to investigate the best constant in the weak type (1, 1) inequality for the Hardy-Littlewood centered maximal operator in dimension one. In dimension bigger than one we also obtain some lower bounds for that constant.     

Averaged topological equations for dispersed two-phase flows

A general relationship between the volume fraction and the specific interfacial area for averaged dispersed two-phase flows is proposed. This relationship, expressed as a basic set of two scalar evolution equations and two vectorial non-uniformity state equations, is an analytical result obtained by a systematic approach using the derivatives of some generalized functions and a local volume-averaging technique. The proposed set of equations was expressed for measurable macroscopic parameters of the system and has the same generality as the averaged transport equations of two-phase flows. By combination of the basic set of equations, called the averaged topological equations (ATEs), second-order ATEs for the volume fraction were found. The second-order ATEs were expressed both by a Lagrangian formulation and by a Eulerian formulation. The importance and physical meaning of the ATEs developed in this study were clarified within the framework of the theory of kinematic waves.     

A thermodynamic analysis on the coincidence of extrema conditions in the sorption equilibrium for ternary polymer systems

Flory-Huggins theory of polymer solutions has been used to express the condition of extrema values in the total sorption, as well as the inversion point in the preferential adsorption parameters for termary polymer systems. Two approaches have been followed, the first considers the binary and ternary interaction parameters independent of polymer concentration and solvent composition. In the second one, this dependence has been introduced. Our attention is focused on the volume fraction of solvent mixture dependence of the above parameters, in order to confirm or not the coincidence between the extrema values and the inversion point. Several cosolvent and cononsolvent ternary polymer systems, have been used to test the validity of the equations obtained. Also, it has been verified, from an experimental point of view, that in cosolvent ternary polymer systems there is coincidence in both compositions while in cononsolvent ternary polymer systems, such coincidence does not appear.     

Excess thermodynamic properties of the 2-propanol + dichloromethane system at 25°C

Densities, viscosities, enthalpies, vapor-liquid equilibria, and surface tensions were determined at 25°C for the 2-propanol+dichloromethane system. From the experimental results excess volumes, viscosities, enthalpies, Gibbs energies, and excess surface tensions were calculated. An attempt has been made to explain the observed deviations from ideal behavior on the basis of intermolecular interactions.     

Correlation between transport and equilibrium properties through the ternary interaction parameter for cosolvent and cononsolvent polymeric systems

A study of the ternary polymer systems dimethyl formamide-ethyl acetate-polystyrene, chloroform-1,4 dioxane-polystyrene and tetrahydrofuran-chloroform-polystyrene was carried out by viscosity and light scattering at 298 K. A good correlation has been found between the excess intrinsic viscosity, unperturbed polymer dimensions, second virial coefficient and the excess Gibbs free energy by using a ternary interaction parameter, dependent on molecular weight. This modification enables the conversion between transport and equilibrium properties.     

Patterns in the precision of quantitative data from multicomponent gas chromatographic or gas chromatographic-mass spectrometric analysis

The dispersion of the quantitative results in the analysis of volatile compounds from multicomponent mixtures by different fractionation techniques (solid-phase microextraction and direct thermal desorption) followed by GC or GC-MS presents nonrandom patterns related to the existence of different factors in the fractionation process or in the chromatographic separation which affect, to a different extent, the recovery of the sample components. Statistical techniques have been used to show the relative importance of these factors. The improvement in data precision achieved by using volatile compound concentration ratios is discussed.     

Poly(2-hydroxyethyl acrylate) hydrogel confined in a hydrophobous porous matrix

A series of interpenetrated polymer networks (IPNs) in which the first component is a porous poly(ethyl methacrylate) (PEMA) hydrophobic network and the second one is a poly(2-hydroxyethyl acrylate) (PHEA) hydrophilic network were synthesized. Equilibrium sorption isotherms can be reduced to a single master curve for all the IPNs when the water absorbed is expressed per gram of PHEA in them. The equilibrium water sorption in immersion is always much smaller than that of pure PHEA. This feature is due to the confining effect of the stiff PEMA matrix. The plasticizing effect of the absorbed water on the PHEA phase was characterized using thermally stimulated depolarization currents, dynamic-mechanical analysis and dielectric relaxation spectroscopy. The results show that the shift of the main relaxation peak towards lower temperatures is unaffected by the presence of the PEMA matrix, and only depends on the water content per gram of PHEA in the IPN.     

Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two‐dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.